Numerical study on natural convection in enclosures with different geometries / Cheong Huey Tyng - Cheong, Huey Tyng (2017)
Natural convection is a heat transfer process which occurs due to temperature differences between a surface and surrounding fluids. Together with fluid flow, natural convective heat transfer has been an important interest for energy-related applications and production industries. The present study deals with natural convection in enclosures with different geometries, which are rectangular, triangular, trapezoidal, oblique and wavy enclosures. Different thermal boundary conditions are taken into account as well. The enclosure is two-dimensional and hence the governing equations are derived using two-dimensional Cartesian coordinate system. The enclosure is filled with fluid-saturated porous medium. Darcy model is used to describe the fluid flow through the porous medium. Different temperature profiles are applied on the sidewall of the enclosure, and appropriate boundary conditions are formulated for all sidewalls. The governing equations and boundary conditions are dimensional, and hence dimensionless method is employed to reduce the equations to dimensionless form. Grid generation method is used to map the non-rectangular domain to a rectangular computational domain. Finite difference approximations are then used to discretize the dimensionless governing equations and boundary conditions. A numerical algorithm is developed to implement the numerical methods proposed. The discretized governing equations and boundary conditions are solved iteratively until the convergence is reached. The solutions are obtained graphically to show the fluid flow and temperature distribution inside the enclosure at steady state. Also, heat transfer rate is calculated to determine the significance of the model. It is observed that the geometry and thermal boundary conditions affect the fluid flow and temperature distribution, as well as the heat transfer rate inside the enclosure. The heat transfer rate increases with Darcy-Rayleigh number. Also, the raise of internal heat generation reduces the heat transfer rate inside the porous enclosure at high Darcy-Rayleigh number. The wavy porous enclosure has the highest heat transfer rate among all enclosure shapes considered. Constant heating also gives higher heat transfer rate compared to other temperature profiles (sinusoidal and linear heating).